bibkey: oeis2025a146557 authors: OEIS Foundation Inc.; Peter Bala; Max Alekseyev year: 2025 title: OEIS A146557 collinear triple divisibility conjecture doi: null url: https://oeis.org/A146557 claim: Peter Bala conjectures that n squared divides A146557(n) when three does not divide n. strata_touched:
- D5/S3/Factorization/CollinearTripleTranslationOrbits license: citation-only triage: anchor
OEIS A146557 collinear triple divisibility conjecture
Directly inspected on September 8, 2026. The entry still states: “Conjecture: if 3 does not divide n then n^2 divides a(n).” It attributes this comment to Peter Bala, July 24, 2025.
The title counts collinear triples of distinct points in Zn x Zn, with no two on a common horizontal or vertical line. The determinant comment specifies a zero determinant for the rows (1,x,u), (1,y,v), (1,z,w), with x,y,z distinct and u,v,w distinct. Subtracting the first row from the other two gives exactly the difference determinant in the formal definition. Triples are counted as unordered sets, consistently with the entry’s initial values 0,0,6,32,200. The matrix comment does not explicitly mention identifying row permutations; literal ordered matrices would overcount these values by six.
The internal page revision line at inspection was
%I #15 Jul 27 2025 11:15:48. An April 8, 2026 entry-specific update date
reported in the implementation brief was not confirmed by this page.
Verified locator
- https://oeis.org/A146557
- https://oeis.org/A146557/internal: title, determinant comment, Peter Bala’s conjecture, and the initial terms.
Proof scope
The formal argument counts unordered three-element finsets and uses the free translation action. It proves the universal assertion for all positive moduli not divisible by three. The website-to-definition identification is documentary; the kernel verifies the explicitly defined mathematical count. The brief reports no independent proof in its searched public indexes. First-publication priority and exhaustive literature coverage are not claimed.